Symmetry and singularity properties of second-order ordinary differential equations of Lie's Type III.

DOI10.1016/j.jmaa.2006.06.006zbMath1121.34091OpenAlexW2039428196MaRDI QIDQ864605

K. Andriopoulos, Peter G. L. Leach

Publication date: 12 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.06.006

zbMATH Keywords

symmetrylinearizationPainlevé property

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (8)

Lie symmetry analysis and similarity solutions for the Jimbo-Miwa equation and generalisations ⋮ Autonomous self-similar ordinary differential equations and the Painlevé connection ⋮ New insights into singularity analysis ⋮ Properties of the Calogero-Degasperis-Ibragimov-Shabat differential sequence ⋮ A Novel Riccati Sequence ⋮ Integrability analysis of the Emden-Fowler equation ⋮ Singularity Analysis and Integrability of a Simplified Multistrain Model for the Transmission of Tuberculosis and Dengue Fever ⋮ Aspects of proper differential sequences of ordinary differential equations

Uses Software

• DIMSYM
• LIE

Cites Work

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• Symmetries of first integrals and their associated differential equations
• On the uniqueness of the Schwarzian and linearisation by nonlocal contact transformation
• DIMSYM and LIE: Symmetry determination packages
• Integration of second order ordinary differential equations not possessing Lie point symmetries
• Symmetries of nonlinear differential equations and linearisation
• Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation
• First integrals for the modified Emden equation q̈+α(t) q̇+q n =0
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• On the singularity analysis of ordinary differential equations invariant under time translation and rescaling
• Hidden symmetries and linearization of the modified Painlevé–Ince equation
• Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view
• The Painleve test, hidden symmetries and the equation y"+yy'+Ky³=0
• Jacobi's Last Multiplier and the Complete Symmetry Group of the Ermakov-Pinney Equation
• The Economy of Complete Symmetry Groups for Linear Higher Dimensional Systems
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0
• LIE, a PC program for Lie analysis of differential equations
• Complete symmetry groups of ordinary differential equations and their integrals: Some basic considerations

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